Method for detecting fluorescent species that are reversibly photoswitchable at a high frequency

ABSTRACT

A method is provided for detecting a fluorescent species that is reversibly photoswitchable at high frequency, and more precisely to a method for detecting at least one reversibly photoswitchable fluorescent species, including a step consisting in illuminating a sample containing a reversibly photoswitchable fluorescent species with a first illuminating light beam, of wavelength λ1, and periodically modulated at an angular frequency ω, and with a second illuminating light beam of wavelength λ2 different from λ1, which is periodically modulated at the angular frequency ω, the second illuminating light beam being modulated in antiphase with respect to the first illuminating light beam.

The invention relates to a method for detecting fluorescent species thatare reversibly photoswitchable at high frequency. Such a method has manyapplications, in particular in chemistry, in biology and in the field ofenvironmental measurements and screening.

The term “species” is understood to mean a chemical species such as amolecule or a complex, or a physical object such as a nanoparticle. Theexpression “reversibly photoswitchable species” is understood to mean aspecies that has at least two distinct states having differentfluorescence properties and that may be made to pass from one state tothe other reversibly under the effect of light. Examples of reversiblyphotoswitchable fluorescent species are the protein “Dronpa” and thecomplex “Spinach-DFHBI” (“Spinach” being an RNA aptamer and DFHPI afluorogenic probe). These species may in particular be used as probes ormarkers. Other examples of reversibly switchable fluorescent species maybe azo derivatives or indeed protein scaffolds.

Fluorescence imaging, and more particularly fluorescence microscopy, hasbecome an indispensable tool in biology, but also in other disciplinessuch as the science of materials. Its applications are however limitedby the ability to observe a signal of interest on a background offluorescence or noise. This problem is particularly acute in animal orplant in vivo imaging applications, in which the fluorescent markers tobe detected are dispersed in a complex autofluorescent and/or scatteringmedium; the useful signal is then hidden in intense background noise.

Another limit on fluorescence imaging and detecting technique resides inthe width of the spectral band of the fluorophores generally employed,with respect to the width of the visible spectral band: it is difficultto selectively detect more than four fluorescent markers in the samesample, because their emission spectra tend to superpose.

To overcome these limits, the patent application WO 2015075209 A1 andthe article by J. Querard et al. “Photoswitching Kinetics andPhase-Sensitive Detection Add Discriminative Dimensions for SelectiveFluorescence Imaging”, Angew. Chem. Int. Ed. 2015, 54, 266-2637 (2015),disclose a method using reversibly photoswitchable fluorescent probes,in which method a sample, containing a photoswitchable fluorophorespecies, is illuminated with a periodically modulated light wave. Thecomponent of the intensity emitted by the fluorophores at the sameangular frequency is then detected, in phase quadrature with respect tothe excitation wave. This method allows certain reversiblyphotoswitchable fluorophores to be selectively detected whileminimizing, under certain conditions that are calculated analyticallydepending on the characteristics of the fluorophore, the noisegenerated, in conventional methods, by autofluorescence and/or diffusionin the medium of the sample. One of the problems of this method residesin the frequency of acquisition of successive images. The variousreversibly photoswitchable fluorescent species used in the prior art areinduced to pass from an activated state to their initial non-activatedstate thermally: the characteristic time of this transition is forexample from 5 to 10 seconds and corresponds to the acquisition time ofan image using this method. This timescale is too long to take asubstantial, biologically relevant number of measurements.

Another prior-art technique is disclosed in the article by Yen-ChengChen et al. (Chen, Y. C., Jablonski, A. E., Issaeva, I., Bourassa, D.,Hsiang, J. C., Fahmi, C. J., & Dickson, R. M., 2015, Optically ModulatedPhotoswitchable Fluorescent Proteins Yield Improved Biological ImagingSensitivity, Journal of the American Chemical Society, 137(40),12764-12767) which proposes a fluorophore-detecting method that uses twomonochromatic sources of laser light of different excitation wavelengthsto achieve heterodyne excitation of a reversibly photoswitchablefluorescent species. This technique proposes an empirical choice of theparameters of measurement of the fluorescence of a species, thispreventing this type of measurement from being easily transposed toother species. In addition, the signal-to-noise ratio during themeasurement of a reversibly photoswitchable fluorescent species is notoptimal. Lastly, the disclosed method does not indicate to a personskilled in the art how to observe two reversibly photoswitchablefluorescent species at the same time.

Yet another prior-art technique that makes it possible to exploit thetemporal dynamic range of a reversibly photoconvertible probe—which isspecific thereto and different from that of interfering fluorophores—toextract a useful signal from the background noise is known as opticallock-in detection (OLID). This technique is described in the article byG. Marriott et al. “Optical lock-in detection imaging microscopy forcontrast-enhanced imaging in living cells”, PNAS, vol. 105, no 46, pages17789-17794 (18 Nov. 2008), and in the article by Y. Yan et al. “Opticalswitch probes and optical lock-in detection (OLID) imaging microscopy:high-contrast fluorescence imaging with living systems”, Biochem J(2011), 411-422 and in the article by C. Petchprayoon et al. “Rationaldesign, synthesis, and characterization of highly fluorescent opticalswitches for high-contrast optical lock-in detection (OLID) imagingmicroscopy in living cells”, Bioorganic & Medicinal Chemistry 19 (2011),1030-1040. One drawback of this technique is that it delivers noquantitative information on the concentration of the reversibly photoconvertible fluorophores.

The invention aims to remedy the aforementioned drawbacks of the priorart, and more particularly to:

image a sample while differentiating a plurality of differentfluorophores;

allow fluorophores to be imaged at high frequency using a techniqueallowing autofluorescence/scattering noise to be removed;

generally, one or more fluorescent probes in a mixture to be selectivelyand quantitatively imaged.

One subject of the invention allowing this aim to be partially orentirely achieved is a method for detecting at least one reversiblyswitchable fluorescent species, including the following steps:

(a) illuminating a sample containing said at least one said reversiblyphotoswitchable fluorescence species with a first illuminating lightbeam, of wavelength λ₁, and periodically modulated at an angularfrequency ω, and with a second illuminating light beam, of λ₂ differentfrom λ₁, periodically modulated at said angular frequency ω;(b) detecting fluorescence radiation emitted by said sample thusilluminated; and(c) extracting the amplitude from the component of the intensity of saidfluorescence radiation that has the same periodicity as saidperiodically modulated first illuminating light beam and that is inphase quadrature therewith;

said second illuminating light beam being modulated in antiphase withrespect to said first illuminating light beam; and

the average intensity of said first illuminating light beam, the averageintensity of said second illuminating light beam, and their angularfrequency ω being chosen so as to get close to a maximum of saidamplitude of the intensity component of said fluorescence radiation. Forexample, the amplitude may have a value equal to at least 75%,preferably 80%, even more preferably 90% of the maximum.

According to one particular embodiment of such a method, at least onesaid reversibly photoswitchable fluorescent species may have a first andsecond chemical state, at least one of said states being fluorescent,said or each said reversibly photoswitchable fluorescent species beingcapable of being converted from said first state to said second statevia a first photo-induced reaction, then of returning to said firststate via a second photo-induced reaction, and said first illuminatinglight beam may have an average intensity I₁ ⁰ and be modulated at anangular frequency ω and said second illuminating light beam may have anaverage intensity I₂ ⁰ with:

(σ_(12,1)+σ_(21,1))I ₁ ⁰=(σ_(12,2)+σ_(21,2))I ₂ ⁰

and

ω=2(σ_(12,1)+σ_(21,1))I ₁ ⁰

where σ_(12,1)I₁ ⁰ and σ_(21,1)I₁ ⁰ are the rate constants of said firstand said second reactions photo-induced by said first illuminating lightbeam, respectively; and where σ_(12,2)I₂ ⁰ and σ_(21,2)I₂ ⁰ are the rateconstants of said first and said second reactions photo-induced by saidsecond illuminating light beam, respectively.

Moreover, the average intensity of said first illuminating light beam,the average intensity of said second illuminating light beam, and theirangular frequency ω may also be chosen so as to ensure a minimumcontrast between said amplitude of the intensity component of saidfluorescence radiation and the amplitude of a fluorescence intensitycomponent having the same periodicity generated by interfering species.

Another subject of the invention is a method for detecting at least tworeversibly photoswitchable fluorescent species having different dynamicproperties, including the following steps:

(a) illuminating a sample containing each said reversiblyphotoswitchable fluorescent species with a first illuminating light beamof wavelength λ₁ and periodically modulated with a first functionsumming at least two first illuminating components that are modulatedwith angular frequencies ωi, each said angular frequency ωi of each saidfirst illuminating component being associated with one said reversiblyphotoswitchable fluorescent species, and being different from the one ormore other said angular frequencies ωi; andilluminating the sample with a second illuminating light beam, ofwavelength λ₂ different from λ₁, and periodically modulated with asecond function summing at least two second illuminating components thatare modulated with said angular frequencies ωi, each said angularfrequency ωi of each said second illuminating component being equal to asaid angular frequency ωi of a said first illuminating component;(b) detecting fluorescence radiation (FLU) emitted by said sample thusilluminated;(c) extracting each (algebraic) amplitude of the component of theintensity of said fluorescence radiation that has the same angularfrequency ωi as each said illuminating component, and that is in phasequadrature with each said first illuminating component;

for each said angular frequency ω_(i), each said second illuminatingcomponent modulated with said angular frequency ω_(i) being in antiphasewith respect to each said first illuminating component modulated withsaid angular frequency ω_(i);

and the average intensity of said first illuminating light beam, theaverage intensity of said second illuminating light beam, and saidangular frequencies being chosen so as to get close to a maximum of eachsaid amplitude of the intensity component of said fluorescenceradiation.

According to particular embodiments of such a method:

Each said reversibly photoswitchable fluorescent species may have afirst and a second chemical state, at least one of said states beingfluorescent, each said reversibly photoswitchable fluorescent speciesbeing capable of being converted from said first state to said secondstate via a first photo-induced reaction, then of returning to saidfirst state via a second photo-induced reaction, and said firstilluminating light beam may have an average intensity I₁ ⁰ and beperiodically modulated with a said first function, and said secondilluminating light beam may have an average intensity I₂ ⁰ with, foreach said reversibly photoswitchable fluorescent species:

(σ_(12,1)+σ_(21,1))I ₁ ⁰=(σ_(12,2)+σ_(21,2))I ₂ ⁰

where σ_(12,1)I₁ ⁰ and σ_(21,1)I₁ ⁰ are the rate constants of said firstand said second reactions photo-induced by said first light beamilluminating said species, respectively; and where σ_(12,2)I₂ ⁰ andσ_(21,2)I₂ ⁰ are the rate constants of said first and said secondreactions photo-induced by said second light beam illuminating saidspecies, respectively.

For each said angular frequency ω_(i) corresponding to one saidreversibly photoswitchable fluorescent species, it is possible for:

ω_(i)=2(σ_(12,1)+σ_(21,1))I ₁ ⁰

where σ_(12,1)I₁ ⁰ and σ_(21,1)I₁ ⁰ are the rate constants of said firstand said second reactions photo-induced by said first light beamilluminating said species, respectively. Advantageously, the ratiobetween at least two said angular frequencies ω_(i) is strictly higherthan 10.

In said step e), said sample may be illuminated by at least onesubstantially monochromatic illuminating light beam.

Said steps b) and c) may be implemented via synchronous detection ofsaid fluorescence radiation.

The method may also include the following step:

d) determining the concentration of said or at least one said reversiblyphotoswitchable fluorescent species from the component of the intensityof said fluorescence radiation which is extracted in said step c).

Said or at least one said reversibly photoswitchable fluorescent speciesis chosen from: a photochromic fluorescent protein; and a complex of abiomolecule with a fluorogenic probe.

The sample may contain biological material.

Yet another subject of the invention is a fluorescence-imaging (and inparticular fluorescence-microscopy) method implementing such a detectingmethod. In this case, said sample may comprise a living organism, and atleast one element chosen from the presence and concentration of a saidreversibly photoswitchable fluorescent species may be measured on thebasis of the component of the intensity of said fluorescence radiationwhich is extracted in said step c), without taking a sample of saidliving organism.

A said illuminating light beam comprises an amount of daylight andwherein said amount of daylight is included in the light intensityreceived by said reversibly photoswitchable fluorescent species butremains less than or equal to the average intensities of saidilluminating light beams.

The invention will be better understood and other advantages, detailsand features thereof will become apparent from the following explanatorydescription, which is given by way of example with reference to theappended drawings, in which:

FIG. 1 illustrates a method for detecting a reversibly photoswitchablefluorescent species P according to the invention;

FIG. 2 illustrates a chart presenting a theoretical calculation of theresponse of a reversibly photoswitchable fluorescent species P in thecase of an embodiment belonging to the prior art;

FIG. 3 illustrates a chart presenting a theoretical calculation of theresponse of a reversibly photoswitchable fluorescent species in anembodiment of the invention;

FIG. 4 illustrates an embodiment of the invention allowing a pluralityof reversibly photoswitchable fluorescent species to be imaged in thesame image detection;

FIG. 5 illustrates a numerical simulation corresponding to thequantification of a reversibly photoswitchable fluorescent species inthe presence of interfering compounds X;

FIG. 6 is a graph illustrating photochemical properties of a set ofreversibly photoswitchable fluorescent species;

FIG. 7 is a set of photographs illustrating an experimental comparisonbetween embodiments of the prior art and an embodiment of the invention;

FIG. 8 illustrates detection of the fluorescence image of a cellaccording to one embodiment of the invention;

FIG. 9 illustrates a system implementing a method according to oneembodiment of the invention.

FIG. 1 illustrates a method for detecting a reversibly photoswitchablefluorescent species P according to the invention. The method comprisesilluminating a sample E with a first illuminating light beam FEX1, ofwavelength λ₁ and a second illuminating light beam FEX2, of wavelengthλ₂ different from λ₁. Each of the illuminating light beams FEX1, FEX2 ispreferably substantially monochromatic, i.e. its spectrum has a singleintensity maximum and/or a spectral width narrower than or equal to 50nm.

The reversibly photoswitchable fluorescent species P has two differentstates that are exchangeable under the action of light. It may be aquestion of a photochromic fluorescent species, or of any other systemthe dynamic behavior of which may be modelled as an exchange between twostates under the action of light; these states may correspond todifferent stereochemical configurations of a molecule, to abound/non-bound state of a complex, etc. In FIG. 1, the firststate—which is thermodynamically more stable—is indicated by 1 andrepresented by a solid square; the second state—which is thermodynamicdynamically less stable—is indicated by 2 and represented by a hollowsquare. These two states possess different brightnesses. For the sake ofsimplicity, by way of nonlimiting example, only the state 1 isconsidered to be significantly fluorescent.

The sample E, and more precisely the species P that it contains, whenilluminated by a first illuminating light beam FEX1 and by a secondilluminating light beam FEX2, emits fluorescent radiation FLU theintensity of which is also modulated and which may be decomposed into:

a component in phase with the first illuminating light beam FEX1, whichcomponent is indicated in the figure by I_(F) ^(in); and

a component in quadrature with the excitation beam, which component isindicated in the figure by I_(F) ^(out). Patent application WO2015075209 A1 discloses the advantage and basis for observation of thecomponent I_(F) ^(out) during the observation of the species P.

The dynamic behavior of a reversibly photoswitchable fluorescent speciesP may be described in the following way. Under the illumination of aspecies P with light of intensity I(t) containing two components I₁(t)and I₂(t), corresponding to a first illuminating light beam FEX1, ofwavelength λ₁ and a second illuminating light beam FEX2, of wavelengthλ₂, respectively, the dynamic behavior of the species P may be describedby the following exchange between two states:

$\begin{matrix}{1\underset{k_{21}{(t)}}{\overset{k_{12}{(t)}}{\rightleftharpoons}}2} & (1)\end{matrix}$

in which the state 1, which is thermodynamically more stable, isconverted, via a photochemical reaction, into a thermodynamically lessstable state 2 with a rate constant k₁₂(t)=σ_(12,1)I₁(t)+σ_(12,2)I₂(t),and may return to the more stable initial state 1 via a photochemicaland/or thermal process with a rate constantk₂₁(t)=σ_(21,1)I₁(t)+σ_(21,2)I₂(t)+k₂₁ ^(Δ), in which σ_(12,1)I₁(t)σ_(12,2)I₂(t), σ_(21,1)I₁(t), σ_(21,2)I₂(t) represent the photochemicalcontributions and k₂₁ ^(Δ) the thermal contribution to the rateconstants, σ_(12,1) being the cross section of photoconversion from thestate 1 to the state 2 for the illumination of the light beam FEX1,σ_(12,2) being the cross section of photoconversion from the state 1 tothe state 2 for the illumination of the light beam FEX2, σ_(21,1) beingthe cross section of photoconversion from the state 2 to the state 1 forthe illumination of the light beam FEX1 and σ_(21,2) being the crosssection of photoconversion from the state 2 to the state 1 for theillumination of the light beam FEX1. All of these constants togetherdefine the behavior of the species P.

The system is assumed to be illuminated uniformly or may be consideredto be uniform at any given time. The variation in the concentrations 1(concentration in state 1 of species P) and 2 (concentration in state 2of the species P) may then be described by the following system ofequations:

$\begin{matrix}{\frac{d\; 1}{dt} = {{{- {k_{12}(t)}}1} + {{k_{21}(t)}2\mspace{14mu} {and}}}} & (2) \\{\frac{d\; 2}{dt} = {{{k_{12}(t)}1} - {{k_{21}(t)}2}}} & (3)\end{matrix}$

Considering the sample E to be suddenly illuminated by two constantilluminating sources, of wavelength λ₁ and λ₂, respectively, theillumination is characterized by the intensity I(t)=I₁ ⁰+I₂ ⁰=I⁰ and therate constants may be written in the form:

k ₁₂(t)=k ₁₂ ⁰ =k _(12,1) ⁰ +k _(12,2) ⁰,  (4)

k ₂₁(t)=k ₂₁ ⁰ =k _(21,1) ⁰ +k _(21,2) ⁰ +k ₂₁ ^(Δ).  (5)

where

k _(12,1) ⁰=σ_(12,1) I ₁ ⁰,  (6)

k _(21,1) ⁰=σ_(21,1) I ₁ ⁰,  (7)

k _(12,2) ⁰=σ_(12,2) I ₂ ⁰,  (8)

k _(21,2) ⁰=σ_(21,2) I ₂ ⁰.  (9)

Considering the initial state to contain only the species 1, theconcentrations 1 and 2 vary as follows:

$\begin{matrix}{{2 - 2^{0}} = {{1^{0} - 1} = {{- 2^{0}}{\exp\left( {- \frac{t}{\tau_{12}^{0}}} \right)}\mspace{14mu} {where}}}} & (10) \\{\tau_{12}^{0} = \frac{1}{k_{12}^{0} + k_{21}^{0}}} & (11)\end{matrix}$

corresponds to the relaxation time of a reversibly photoswitchablefluorophore and 1⁰ and 2⁰ to the concentrations 1 and 2 in thephotostationary state achieved at the time τ₁₂ ⁰. Thus:

$\begin{matrix}{1^{0} = {{P_{tot} - 2^{0}} = {\frac{1}{1 + K_{12}^{0}}P_{tot}\mspace{14mu} {where}\text{:}}}} & (12) \\{K_{12}^{0} = \frac{k_{12}^{0}}{k_{21}^{0}}} & (13)\end{matrix}$

and the total concentration of the species P is P_(tot)=1+2.

It is possible to analyze the response in terms of fluorescent emission,or fluorescence radiation FLU of a reversibly photoswitchablefluorescent species P when it is subjected to two periodically modulatedilluminating light beams FEX1, FEX2, corresponding to embodiments of theinvention.

Generally, if a reversibly photoswitchable fluorescent species P issubjected to an illumination comprising two components: a periodicillumination I₁(t) at the wavelength λ₁ and an illumination I₂(t) at thewavelength λ₂, said illumination may be constant, this corresponding toan embodiment not according to the invention, or periodically modulated,this corresponding to embodiments of the invention. It is possible towrite, in the most general case:

I(t)=I ₁(t)+I ₂(t)  (35)

and I _(j)(t)=I _(j) ⁰[1+αh _(j)(t)]  (36)

with j=1 or 2. In equation (36), a corresponds to the amplitude of thelight modulation and h_(j)(t) corresponds to periodic functions.Equations (4) and (5) here become:

k ₁₂(t)=k _(12,1) ⁰[1+αh ₁(t)]+k _(12,2) ⁰[1+αh ₂(t)]  (37)

and k ₂₁(t)=k _(21,1) ⁰[1+αh ₁(t)]+k _(21,2) ⁰[1+αh ₂(t)]+k ₂₁^(Δ).  (38)

By introducing a function ƒ(t), it is possible to write the expressionfor the concentrations in the following way:

2=2⁰+αƒ(t)  (39)

and 1=1⁰−αƒ(t).  (40)

The system of differential equations governing the variation as afunction of time of the concentrations 1 and 2 may be solved withequations (2) and (3) to obtain:

$\begin{matrix}{{\frac{{df}(x)}{dx} = {{- {f(x)}} + {\left\lbrack {_{1} - {_{1}{f(x)}}} \right\rbrack {h_{1}(x)}} + {\left\lbrack {_{2} + {_{2}{f(x)}}} \right\rbrack {h_{2}(x)}}}}{{where}\text{:}}} & (41) \\{x = \frac{t}{\tau_{12}^{0}}} & (42) \\{_{1} = {\rho_{12}^{0}\Delta_{12,1}^{0}\tau_{12}^{0}}} & (43) \\{_{1} = {{\alpha \left( {\sigma_{12,1} + \sigma_{21,1}} \right)}I_{1}^{0}\tau_{12}^{0}}} & (44) \\{_{2} = {\rho_{12}^{0}\Delta_{12,2}^{0}\tau_{12}^{0}}} & (45) \\{_{2} = {{\alpha \left( {\sigma_{12,2} + \sigma_{21,2}} \right)}I_{2}^{0}\tau_{12}^{0}\mspace{14mu} {and}\mspace{14mu} {where}\text{:}}} & (46) \\{\rho_{12}^{0} = {{k_{12}^{0}1^{0}} = {k_{21}^{0}2^{0}}}} & (47) \\{\Delta_{12,1}^{0} = {\frac{k_{12,1}^{0}}{k_{12,1}^{0} + k_{12,2}^{0}} - \frac{k_{21,1}^{0}}{k_{21,1}^{0} + k_{21,2}^{0} + k_{21}^{\Delta}}}} & (48) \\{\Delta_{12,2}^{0} = {\frac{k_{12,2}^{0}}{k_{12,1}^{0} + k_{12,2}^{0}} - \frac{k_{21,2}^{0}}{k_{21,1}^{0} + k_{21,2}^{0} + k_{21}^{\Delta}}}} & (49)\end{matrix}$

respectively designate the speed of the reaction corresponding toequation (1) in the stationary state (with 1⁰ and 2⁰ given by equation(12)) and the differences in the relative contributions of the averagesof the modulated illuminations (I₁ ⁰ and I₂ ⁰, respectively) to the rateconstants respectively leading to from state 1 to state 2 or from state2 to state 1.

After the relaxation time τ₁₂ ⁰, a steady-state regime is entered into,in which ƒ(x) is a continuous periodic function. More generally, ƒ(x)may be a periodic function. In the various embodiments of the invention,an illuminating light beam FEX1, FEX2 may be modulated with afundamental angular frequency ω or two fundamental angular frequencies(ω₁ and ω₂) or at least two fundamental angular frequencies, each of thevarious fundamental angular frequencies being denoted, in this case, bya generic term ω_(i).

In a first case, the Fourier series corresponding to ƒ(x) may be writtenin the form:

$\begin{matrix}{{f\left( {\theta \; x} \right)} = {a^{0} + {\sum\limits_{n = 1}^{+ \infty}{\left\lbrack {{a^{n,\cos}{\cos \left( {n\; \theta \; x} \right)}} + {b^{n,\sin}{\sin \left( {n\; \theta \; x} \right)}}} \right\rbrack \mspace{14mu} {where}\text{:}}}}} & (50) \\{{\theta = {\omega\tau}_{12}^{0}},} & (51)\end{matrix}$

and where a^(n,cos) and b^(n,sin) designate the amplitudes of the nthcomponents of the Fourier series.

In the second case, the Fourier series corresponding to ƒ(x) may bewritten in the form:

$\begin{matrix}{{f\left( {{\theta_{1}x},{\theta_{2}x}} \right)} = {a^{0} + {\sum\limits_{n = {- \infty}}^{+ \infty}{\sum\limits_{m = {- \infty}}^{+ \infty}\left\{ {{a^{n,m,\cos}{\cos \left\lbrack {\left( {{n\; \theta_{1}} + {m\; \theta_{2}}} \right)x} \right\rbrack}} + {b^{n,m,\sin}{\sin \left\lbrack {\left( {{n\; \theta_{1}} + {m\; \theta_{2}}} \right)x} \right\rbrack}}} \right\}}}}} & (52) \\{\mspace{79mu} {{where}\text{:}}} & \; \\{\mspace{79mu} {{\theta_{1} = {\omega_{1}\tau_{12}^{0}}},}} & (53) \\{\mspace{79mu} {\theta_{2} = {\omega_{2}\tau_{12}^{0}}}} & (54)\end{matrix}$

and where a⁰, a^(n,m,cos) and b^(n,m,sin) correspond to the amplitudesof the 0-th and of the {n,m}-th components of the Fourier series. a⁰and/or a^(n,m,cos) and/or b^(n,m,sin) may be extracted from equation(41) by identifying components of the same order.

All of the obtained equations may be transformed so as to make theconcentration modulations explicit for all the angular frequencies. Itis then possible to write:

$\begin{matrix}{\mspace{20mu} {2 = {2^{0} + {\alpha {\sum\limits_{n = 1}^{+ \infty}\left\lbrack {{2^{n,{{si}\; n}}{\sin \left( {n\; \theta \; x} \right)}} + {2^{n,{{co}\; s}}{\cos \left( {n\; \theta \; x} \right)}}} \right\rbrack}}}}} & (55) \\{\mspace{20mu} {{1 = {1^{0} - {\alpha {\sum\limits_{n = 1}^{+ \infty}\left\lbrack {{2^{n,{{si}\; n}}{\sin \left( {n\; \theta \; x} \right)}} + {2^{n,{{co}\; s}}{\cos \left( {n\; \theta \; x} \right)}}} \right\rbrack}}}}\mspace{20mu} {where}}} & (56) \\{\mspace{20mu} {{2^{0} = {2^{0} + {\alpha \; a^{0}}}},}} & (57) \\{\mspace{20mu} {{1^{0} = {1^{0} - {\alpha \; a^{0}}}},}} & (58) \\{\mspace{20mu} {{2^{n,{{si}\; n}} = {{- 1^{n,{{si}\; n}}} = b^{n,{{si}\; n}}}},}} & (59) \\{\mspace{20mu} {2^{n,{{co}\; s}} = {{- 1^{n,{{co}\; s}}} = {{a^{n,{{co}\; s}}.\mspace{20mu} {or}}\mspace{14mu} {indeed}\text{:}}}}} & (60) \\{2 = {2^{0} + {\alpha {\sum\limits_{n = {- \infty}}^{+ \infty}{\sum\limits_{m = {- \infty}}^{+ \infty}\left\{ {{2^{n,m,{{si}\; n}}{\sin \left\lbrack {\left( {{n\; \theta_{1}} + {m\; \theta_{2}}} \right)x} \right\rbrack}} + {2^{n,m,{{co}\; s}}{\cos \left\lbrack {\left( {{n\; \theta_{1}} + {m\; \theta_{2}}} \right)x} \right\rbrack}}} \right\}}}}}} & (61) \\{1 = {1^{0} - {\alpha {\sum\limits_{n = {- \infty}}^{+ \infty}{\sum\limits_{m = {- \infty}}^{+ \infty}\left\{ {{2^{n,m,{{si}\; n}}{\sin \left\lbrack {\left( {{n\; \theta_{1}} + {m\; \theta_{2}}} \right)x} \right\rbrack}} + {2^{n,m,{{co}\; s}}{\cos \left\lbrack {\left( {{n\; \theta_{1}} + {m\; \theta_{2}}} \right)x} \right\rbrack}}} \right\}}}}}} & (62) \\{\mspace{20mu} {{where}\text{:}}} & \; \\{\mspace{20mu} {{2^{0} = {2^{0} + {\alpha \; a^{0}}}},}} & (63) \\{\mspace{20mu} {{1^{0} = {1^{0} - {\alpha \; a^{0}}}},}} & (64) \\{\mspace{20mu} {{2^{n,m,{{si}\; n}} = {{- 1^{n,m,{{si}\; n}}} = b^{n,m,{{si}\; n}}}},}} & (65) \\{\mspace{20mu} {2^{n,m,{{co}\; s}} = {{- 1^{n,m,{{co}\; s}}} = {a^{n,m,\; {{co}\; s}}.}}}} & (66)\end{matrix}$

It is also possible to express the fluorescence intensity. Equation (67)defines the observable corresponding to observation at the wavelengthλ_(j) withj=1 or 2:

O _(j)(t)=Q _(1,j)1(t)+Q _(2,j)2(t)  (67)

Extracting the fluorescence emission I_(f)(t) gives equation (68):

I _(F)(t)=O ₁(t)I ₁(t)+O ₂(t)I ₂(t).  (68)

Thus, with the time dependence given by equations (55) and (56):

O j  ( t ) = j 0 + ∑ n = 1 ∞  [ j n , si   n  sin  ( n   θ   x) + j n , co   s  cos  ( n   θ   x ) ] .  with  : ( 69 ) j 0 =Q 1 , j  1 0 + Q 2 , j  2 0 = Q 1 , j  1 0 + Q 2 , j  2 0 + ( Q 2 ,j - Q 1 , j )   α   a 0 ( 70 ) j n , si   n = ( Q 2 , j - Q 1 , j)  α   b n , si   n ( 71 ) j n , co   s = ( Q 2  j - Q 1 , j ) α   a n , co   s   and ( 72 ) I F  ( t ) = + ∑ n = 1 ∞  [  sin ( n   θ   x ) +  cos  ( n   θ   x ) ] . ( 73 )

Whereas the expressions for the amplitudes of the terms O_(j)(t) aregeneric, the expressions for the amplitudes of the terms I_(F)(t) varywith the time dependency of the illumination.

With the time dependencies 1(t) and 2(t) given by equations (61) and(62):

O j  ( t ) = j 0 + ∑ n = - ∞ + ∞  ∑ m = - ∞ + ∞  { j n , m , si   n sin  [ ( n   θ 1 + m   θ 2 )  x ] + j n , m , co   s  cos  [( n   θ 1 + m   θ 2 )  x ] } ( 74 )  with  :  j 0 = Q 1 , j  10 + Q 2 , j  2 0 + ( Q 2 , j - Q 1 , j )  α   a 0 ( 75 )  j n , m ,si   n = ( Q 2 , j - Q 1 , j )  α   b n , m , si   n ( 76 )  j n, m , co   s = ( Q 2 , j - Q 1 , j )  α   a n , m , co   s ( 77 ) and I F  ( t ) = + ∑ n = - ∞ + ∞  ∑ m = - ∞ + ∞  {  sin  [ ( n  θ 1 + m   θ 2 )  x ] +  cos  [ ( n   θ 1 + m   θ 2 )  x ] }. ( 78 )

in which, likewise, the expressions for the amplitudes of the termsO_(j)(t) are generic, the expressions for the amplitudes of the termsI_(F)(t) vary with the time dependency of the illumination.

The inventors first of all considered cases in which the modulations ofthe two amplitudes of the illuminating light beams are small, anddenoted ε instead of α below. This case allows the equations to belinearized and analytical expressions to be derived.

In prior-art embodiments, one of the two illuminating light beams ismodulated sinusoidally (for example the illuminating light beam FEX1 atthe wavelength λ₁, which oscillates about an average intensity I₁ ⁰, atthe angular frequency ω and with a small amplitude εI₁ ⁰ (ε<<1)) anilluminating light beam of constant intensity I₂ ⁰ and of wavelength λ₂being superposed therewith. Then:

I(t)=I ₁ ⁰[1+ε sin(ωt)]+I ₂ ⁰  (79)

h ₁(t)=sin(ωt)  (80)

h ₂(t)=0.  (81)

Developing to the first order the expression for the luminous switching,equation (41) becomes:

$\begin{matrix}{\frac{{df}\left( {\theta \; x} \right)}{dx} = {{- {f\left( {\theta \; x} \right)}} + {a_{1}{h_{1}\left( {\theta \; x} \right)}}}} & (82)\end{matrix}$

After the relaxation time τ₁₂ ⁰ given by equation (11), it is possibleto derive:

$\begin{matrix}{\mspace{20mu} {2^{0} = 2^{0}}} & (83) \\{\mspace{20mu} {1^{0} = 1^{0}}} & (84) \\{2^{1,{{si}\; n}} = {{- 1^{1,{{si}\; n}}} = {\frac{a_{1}}{1 + \theta^{2}} = {{\rho_{12}^{0}\tau_{12}^{0}\Delta_{12,1}^{0}\frac{1}{1 + \left( {\omega \; \tau_{12}^{0}} \right)^{2}}} = {\Delta_{12,1}^{0}\frac{K_{12}^{0}}{\left( {1 + K_{12}^{0}} \right)^{2}}\frac{1}{1 + \left( {\omega \; \tau_{12}^{0}} \right)^{2}}P_{tot}}}}}} & (85) \\{2^{1,{{co}\; s}} = {{- 1^{1,{{co}\; s}}} = {{- \frac{a_{1}\theta}{1 + \theta^{2}}} = {{{- \rho_{12}^{0}}\tau_{12}^{0}\Delta_{12,1}^{0}\frac{\omega \; \tau_{12}^{0}}{1 + \left( {\omega \; \tau_{12}^{0}} \right)^{2}}} = {{- \Delta_{12,1}^{0}}\frac{K_{12}^{0}}{\left( {1 + K_{12}^{0}} \right)^{2}}\frac{\omega \; \tau_{12}^{0}}{1 + \left( {\omega \; \tau_{12}^{0}} \right)^{2}}P_{tot}}}}}} & (86) \\{\mspace{20mu} {{and}\text{:}}} & \; \\{{= {{\left( {{Q_{1,1}1^{0}} + {Q_{2,1}2^{0}}} \right)I_{1}^{0}} + {\left( {{Q_{1,2}1^{0}} + {Q_{2,2}2^{0}}} \right)I_{2}^{0}}}},} & (87) \\{= {ɛ\left\{ {{\left( {{Q_{1,1}1^{0}} + {Q_{2,1}2^{0}}} \right)I_{1}^{0}} + {\left\lbrack {{\left( {Q_{1,1} - Q_{2,1}} \right)I_{1}^{0}} + {\left( {Q_{1,2} - Q_{2,2}} \right)I_{2}^{0}}} \right\rbrack 1^{1,{{si}\; n}}}} \right\}}} & (88) \\{\mspace{20mu} {= {{ɛ\left\lbrack {{\left( {Q_{1,1} - Q_{2,1}} \right)I_{1}^{0}} + {\left( {Q_{1,2} - Q_{2,2}} \right)I_{2}^{0}}} \right\rbrack}{1^{1,{{co}\; s}}.}}}} & (89)\end{matrix}$

Using two different wavelengths, the exchanges between states 1 and 2are essentially governed by the photochemical contributions if theaverage intensities (I₁ ⁰, I₂ ⁰) are chosen so that: σ_(21,1)I₁⁰+σ_(21,2)I₂ ⁰>>k₂₁ ^(Δ).

FIG. 2 shows a chart illustrating a theoretical calculation of theresponse of a reversibly photoswitchable fluorescent species P in thecase of an embodiment belonging to the prior art. The chart of FIG. 2illustrates the value of the normalized amplitude of the oscillations inphase quadrature for a concentration 1 (|1_(norm)^(1,cos)|=|1^(1,cos)/P_(tot)|), as a function of control parameters I₂⁰/I₁ ⁰ and ω/I₁ ⁰. This case corresponds to an illuminating light beamFEX1 of wavelength λ₁ oscillating about an average intensity I₁ ⁰ at theangular frequency ω and with a small amplitude εI₁ ⁰ (ε<<1), with whichan illuminating light beam of constant intensity I₂ ⁰ and of wavelengthλ₂ is superposed. The reversibly switchable fluorescent species P inquestion is “Dronpa-2”, for which the inventors have measured the rateparameters, these corresponding to σ_(12,1)=196 m²·mol⁻¹, σ_(21,1)=0m²·mol⁻¹, σ_(12,2)=0 m²·mol⁻¹, σ_(21,2)=413 m²·mol⁻¹ and k₂₁^(Δ)=1,4.10⁻² s⁻¹, with

$I_{1}^{0} = {100\; {\frac{k_{21}^{\Delta}}{\sigma_{12,1} + \sigma_{21,1}}.}}$

In this case, |1_(norm) ^(1,cos)| has a single maximum when the twofollowing conditions of resonance are met:

(σ_(12,1)+σ_(21,1))I ₁ ⁰=(σ_(12,2)+σ_(21,2))I ₂ ⁰ and  (90)

ω=2(σ_(12,1)+σ_(21,1))I ₁ ⁰.  (91)

This optimization results in an optimization that is independent of theterms α₁ and θ/[(1+θ²] of equation (86). α₁ corresponds to the variationΔ2⁰ in the steady-state regime 2⁰ after an amplitude jump ΔI₁ ⁰=εI₁ ⁰.It is maximized when the rate constants of the photochemical reactionsinduced by the two illuminating light beams are equal. The secondoptimized term, θ/[1+θ²], is maximized by adjusting the angularfrequency ω to the relaxation time τ₁₂ ⁰ so as to obtain θ=1. Whenω>>1/τ₁₂ ⁰, the exchange is slow with respect to variations in theillumination and the pair {1,2} has no time to respond, so as to makethe terms i^(1,sin) and i^(1,cos) disappear. In contrast, when ω>>1/τ₁₂⁰, i^(1,cos) cancels out and the concentrations 1 and 2 oscillate inphase with the modulation of the illumination. More generally, and inall the embodiments of the invention, the average intensity of saidfirst illuminating light beam (FEX1), the average intensity of saidsecond illuminating light beam (FEX2), and their angular frequency ω arechosen so as to maximize the amplitude of the intensity component ofsaid fluorescence radiation (FLU) in phase quadrature with the firstilluminating light beam.

In embodiments of the invention, the two illuminating light beams FEX1,FEX2 are modulated sinusoidally (or more generally periodically), at thesame angular frequency ω. The inventors have discovered that it ispossible to increase the amplitude, to the first order, of the responseto the illuminating modulations of a species P with respect to the casein which the second illuminating light beam excites a species P with aconstant intensity. By way of example, I(t) is considered to comprise asuperposition of two sinusoidal modulations of small amplitudes: on theone hand, at the wavelength λ₁ about the average intensity I₁ ⁰ and atthe angular frequency ω, and on the other hand, at the wavelength λ₂about the average intensity I₂ ⁰ and at the angular frequency ω. Thus:

I(t)=I ₁ ⁰[1+εh ₁(t)]+I ₂ ⁰[1+εh ₂(t)],  (92)

h ₁(t)=sin(ωt),  (93)

h ₂(t)=sin(ωt+φ)  (94)

with ε<<1.

Developing to the first order the switching caused by the illumination,f(x)=f₁(θx)+f₂(θx) is a solution of equation (41) when f₁(θx) and f₂(θx)are solutions of the following equation (95):

$\begin{matrix}{\frac{{df}_{j}\left( {\theta \; x} \right)}{dx} = {{- {f_{j}\left( {\theta \; x} \right)}} + {a_{j}{h_{j}\left( {\theta \; x} \right)}}}} & (95)\end{matrix}$

with j=1 or 2, respectively. It will be noted that this equation issimilar to equation (82). After the relaxation time τ₁₂ ⁰ given byequation (11), it is possible to derive:

$\begin{matrix}{{2^{0} = 2^{0}},} & (96) \\{{1^{0} = 1^{0}},} & (97) \\{{2^{1,{{si}\; n}} = {{- 1^{1,{{si}\; n}}} = {\frac{a_{1}}{1 + \theta^{2}} + \frac{a_{2}\left( {{\cos \; \phi} + {\theta \; \sin \; \phi}} \right)}{1 + \theta^{2}}}}},} & (98) \\{2^{1,{{co}\; s}} = {{- 1^{1,{{co}\; s}}} = {{- \frac{a_{1}\theta}{1 + \theta^{2}}} + \frac{a_{2}\left( {{\sin \; \phi} - {\theta \; \cos \; \phi}} \right)}{1 + \theta^{2}}}}} & (99)\end{matrix}$

For the species P used in the embodiments of the invention,nonlimitingly, the photochemically induced transition from the state 1to that state 2 (or from state 2 to state 1, respectively) is governedexclusively by an illumination at the wavelength λ₁ (or λ₂,respectively). Considering the rate constant of the reaction that causesthe transition from state 2 to state 1 to be mainly governed byphotochemistry, it is possible to deduce that a₁=−a₂. Equations 98 and99 become:

$\begin{matrix}{{2^{1,{s\; i\; n}} = {{- 1^{1,{s\; i\; n}}} = {\frac{a_{1}}{1 + \theta^{2}}\left\lbrack {\left( {1 - {\cos \; \phi}} \right) - {\theta \; \sin \; \phi}} \right\rbrack}}},} & (100) \\{2^{1,{{co}\; s}} = {{- 1^{1,{{co}\; s}}} = {- {\frac{a_{1}}{1 + \theta^{2}}\left\lbrack {{\theta \left( {1 - {\cos \; \phi}} \right)} + {\sin \; \phi}} \right\rbrack}}}} & (101)\end{matrix}$

Equations (100) and (101) show that φ=π is typically favourable forincreasing the amplitudes of the fluorescence response. Equations (100)and (101) then become:

$\begin{matrix}{2^{1,{{si}\; n}} = {{- 1^{1,{{si}\; n}}} = \frac{2a_{1}}{1 + \theta^{2}}}} & (102) \\{2^{1,{{co}\; s}} = {{- 1^{1,{{co}\; s}}} = {- \frac{2a_{1}\theta}{1 + \theta^{2}}}}} & (103)\end{matrix}$

and the terms of the fluorescence intensities are:

=(Q _(1,1)1⁰ +Q _(2,1)2⁰)I ₁ ⁰+(Q _(1,2) ⁰ +Q _(2,2)2⁰)I ₂ ⁰  (104)

=ε{[(Q _(1,1)1⁰ +Q _(2,1)2⁰)I ₁ ⁰−(Q _(1,2)1⁰ +Q _(2,2)2⁰)I ₂ ⁰]}+ε{[(Q_(1,1) −Q _(2,1))I ₁ ⁰+(Q _(1,2) −Q _(2,2))I ₂ ⁰]1^(1,sin)}  (105)

=ε[(Q _(1,1) −Q _(2,1))I ₁ ⁰+(Q _(1,2) −Q _(2,2))I ₂ ⁰]1^(1,cos).  (106)

In particular, the inventors have discovered that the illuminationvariation corresponding to equation (92) with φ=π produces,qualitatively, the same results for

as a luminous excitation governed by equation (79) but with an amplitudethat, in theory, is two times higher. This increase in amplitude allowsa number of prior-art technical problems to be solved as it allows aspecies P obeying the resonance conditions given by equations (90) and(91) to be selectively imaged with a higher temporal resolution and ahigher signal-to-noise ratio. More generally, in all of the embodimentsof the invention, in which embodiments a first illuminating light beamFEX1 is modulated periodically at an angular frequency ω and a secondilluminating light beam is modulated periodically at the same angularfrequency ω, the second illuminating light beam FEX2 is modulated inantiphase, i.e. at φ=π with respect to the first illuminating light beamFEX1.

FIG. 3 shows a chart illustrating a theoretical calculation of theresponse of a reversibly photoswitchable fluorescent species P in anembodiment of the invention. The chart of FIG. 3 illustrates the valueof the normalized amplitude of the oscillations in phase quadrature fora concentration 1 (|1_(norm) ^(1,cos)|=|1^(1,cos)/P_(tot)|), as afunction of control parameters I₂ ⁰/I₁ ⁰ and ω/I₁ ⁰. This casecorresponds to an illuminating light beam FEX1 of wavelength λ₁oscillating about an average intensity I₁ ⁰ at the angular frequency ωand with a small amplitude εI₁ ⁰ (ε<1), with which an illuminating lightbeam FEX2 of wavelength λ₂ oscillating about an average intensity I₂ ⁰at the angular frequency ω and with a small amplitude εI₂ ⁰ (ε<1), issuperposed. The other parameters are similar to the parameters used inthe embodiment corresponding to FIG. 2. In this case, |1_(norm)^(1,cos)| has a single maximum when the two conditions of resonance,corresponding to equations (90) and (91), are met, as in the embodimentillustrated in FIG. 2, but the norm of which is substantially two timeshigher, this resulting in an increase of a factor of 4 in thesignal-to-noise ratio. The signal-to-noise ratio could be considered asignal-to-interference (SIR) ratio.

FIG. 4 illustrates an embodiment of the invention allowing a pluralityof reversibly photoswitchable fluorescent species to be imaged duringthe same image detection. In this embodiment of the invention, a firstilluminating light beam FEX1 of wavelength λ₁ is modulated periodicallywith a first function summing at least two first illuminating componentsthat are modulated with angular frequencies ω_(i), the angularfrequencies being different from one another. In the nonlimiting exampleillustrated in FIG. 4, the first illuminating light beam FEX1 ismodulated with a function summing an angular-frequency component ω₁ andan angular-frequency component ω₂. Each of the angular frequencies ω_(i)is associated, or corresponds, to a reversibly photoswitchablefluorescent species of the imaged sample E. In the case illustrated inFIG. 4, the angular frequency ω₁ corresponds to the species Prepresented by a solid square and an open square, and the angularfrequency ω₂ corresponds to the species P′ represented by a solidhexagon and an open hexagon. The species P″ represented by a circlecorresponds to no particular angular frequency. The sample is alsoilluminated with a second illuminating light beam FEX2 of wavelength λ₂,which is modulated periodically with a second function summing at leasttwo first illuminating components that are modulated with the sameangular frequencies ω_(i), i.e. in the nonlimiting case of FIG. 4, withthe angular frequencies ω₁ and ω₂.

Analytically, it is possible to consider, nonlimitingly, theilluminating intensity I(t) to be a superposition of two small-amplitudesinusoidal modulations, at the angular frequencies ω₁ and ω₂, whichoscillate about an average intensity I₁ ⁰, at the wavelength λ₁, andabout an average intensity I₂ ⁰, at the wavelength λ₂. In otherembodiments of the invention, the modulations may be periodic, ofdifferent forms, and of larger amplitude. It is considered that:

I(t)=I ₁ ⁰[1+εh ₁(t)]+I ₂ ⁰[1+εh ₂(t)],  (121)

h ₁(t)=sin(ω₁ t)+β sin(ω₂ t),  (122)

h ₂(t)=−sin(ω₁ t)−β sin(ω₂ t),  (123)

with ε<<1. In this case, I₁ ⁰[1+εh₁(t)] corresponds to a first functionand I₂ ⁰[1+εh₂(t)] corresponds to a second function.

Developing to the first order the switching caused by the illumination,f(x)=f₁(θ₁x)+βf₂(θ₂x) is a solution of equation (41) when f₁(θ₁x) andf₂(θ₂x) are solutions of the following equation (124):

$\begin{matrix}{\frac{{df}_{j}\left( {\theta_{j}x} \right)}{dx} = {{- {f_{j}\left( {\theta_{j}x} \right)}} + {\left( {a_{1} - a_{2}} \right){\sin \left( {\theta_{j}x} \right)}}}} & (124)\end{matrix}$

with j=1 or 2, respectively. After the relaxation time τ₁₂ ⁰, it ispossible to derive:

$\begin{matrix}{{2^{0} = 2^{0}},} & (125) \\{{1^{0} = 1^{0}},} & (126) \\{{2^{1,0,{{si}\; n}} = {{- 1^{1,0,{{si}\; n}}} = \frac{\left( {a_{1} - a_{2}} \right)}{1 + \theta_{1}^{2}}}},} & (127) \\{{2^{1,0,{{co}\; s}} = {{- 1^{1,0,{{co}\; s}}} = {- \frac{\left( {a_{1} - a_{2}} \right)\theta_{1}}{1 + \theta_{1}^{2}}}}},} & (128) \\{2^{0,1,{{si}\; n}} = {{- 1^{0,1,{{si}\; n}}} = {\beta \frac{\left( {a_{1} - a_{2}} \right)}{1 + \theta_{2}^{2}}\mspace{14mu} {and}}}} & (129) \\{2^{0,1,{{co}\; s}} = {{- 1^{0,1,{{co}\; s}}} = {{- \beta}\; \frac{\left( {a_{1} - a_{2}} \right)\theta_{2}}{1 + \theta_{2}^{2}}}}} & (130)\end{matrix}$

Equations (127) to (130) lead to:

$\begin{matrix}{2^{1,0,{{si}\; n}} = {{- 1^{1,0,{{si}\; n}}} = {\frac{\rho_{12}^{0}{\tau_{12}^{0}\left( {\Delta_{12,1}^{0} - \Delta_{12,2}^{0}} \right)}}{1 + \left( {\omega_{1}\tau_{12}^{0}} \right)^{2}} = {\frac{K_{12}^{0}}{\left( {1 + K_{12}^{0}} \right)^{2}}\frac{\left( {\Delta_{12,1}^{0} - \Delta_{12,2}^{0}} \right)}{1 + \left( {\omega_{1}\tau_{12}^{0}} \right)^{2\;}}P_{tot}}}}} & (131) \\{2^{1,0,{{co}\; s}} = {{- 1^{1,0,{{co}\; s}}} = {{- \frac{\omega_{1}\tau_{12}^{0}\rho_{12}^{0}{\tau_{12}^{0}\left( {\Delta_{12,1}^{0} - \Delta_{12,2}^{0}} \right)}}{1 + \left( {\omega_{1}\tau_{12}^{0}} \right)^{2}}} = {{- \frac{K_{12}^{0}}{\left( {1 + K_{12}^{0}} \right)^{2\;}}}\frac{\omega_{1}{\tau_{12}^{0}\left( {\Delta_{12,1}^{0} - \Delta_{12,2}^{0}} \right)}}{1 + \left( {\omega_{1}\tau_{12}^{0}} \right)^{2}}P_{tot}}}}} & (132) \\{2^{0,1,{{si}\; n}} = {{- 1^{0,1,{{si}\; n}}} = {{\beta \; \frac{\rho_{12}^{0}{\tau_{12}^{0}\left( {\Delta_{12,1}^{0} - \Delta_{12,2}^{0}} \right)}}{1 + \left( {\omega_{2}\tau_{12}^{0}} \right)^{2}}} = {\beta \; \frac{K_{12}^{0}}{\left( {1 + K_{12}^{0}} \right)^{2}}\frac{\left( {\Delta_{12,1}^{0} - \Delta_{12,2}^{0}} \right)}{1 + \left( {\omega_{2}\tau_{12}^{0}} \right)^{2}}P_{tot}}}}} & (133) \\{2^{0,1,{{co}\; s}} = {{- 1^{0,1,{{co}\; s}}} = {{{- \beta}\; \frac{\omega_{2}\tau_{12}^{0}\rho_{12}^{0}{\tau_{12}^{0}\left( {\Delta_{12,1}^{0} - \Delta_{12,2}^{0}} \right)}}{1 + \left( {\omega_{2}\tau_{12}^{0}} \right)^{2}}} = {{- \beta}\; \frac{K_{12}^{0}}{\left( {1 + K_{12}^{0}} \right)^{2}}\frac{\omega_{2}{\tau_{12}^{0}\left( {\Delta_{12,1}^{0} - \Delta_{12,2}^{0}} \right)}}{1 + \left( {\omega_{2}\tau_{12}^{0}} \right)^{2}}P_{tot}}}}} & (134)\end{matrix}$

and the terms associated with the oscillating fluorescence emissionsare:

=(Q _(1,1)1⁰ +Q _(2,1)2⁰)I ₁ ⁰+(Q _(1,2)1⁰ +Q _(2,2)2⁰)I ₂ ⁰,  (135)

=ε{(Q _(1,1)1⁰ +Q _(2,1)2⁰)I ₁ ⁰−(Q _(1,2)1⁰ +Q _(2,2)2⁰)I ₂ ⁰}+ε{[(Q_(1,1) −Q _(2,1))I ₁ ⁰+(Q _(1,2) −Q _(2,2))I ₂ ⁰]1^(1,0,sin)},  (136)

=ε[(Q _(1,1) −Q _(2,1))I ₁ ⁰+(Q _(1,2) −Q _(2,2))I ₂⁰]1^(1,0,cos),  (137)

=εβ{(Q _(1,1)1⁰ +Q _(2,1)2⁰)I ₁ ⁰−(Q _(1,2)1⁰ +Q _(2,2)2⁰)I ₂ ⁰}+ε{[(Q_(1,1) −Q _(2,1))I ₁ ⁰+(Q _(1,2) −Q _(2,2))I ₂ ⁰]1^(0,1,sin} and)  (138)

=ε[(Q _(1,1) −Q _(2,1))I ₁ ⁰+(Q _(1,2) −Q _(2,2))I ₂⁰)]1^(0,1,cos).  (139)

In this embodiment, the fluorescence response of the sample E to thesuperposition of two small-amplitude antiphase modulations at twodifferent angular frequencies ω₁ and ω₂ allows the embodiments of theinvention corresponding to FIGS. 1 and 3 to be used to simultaneouslyand selectively detect two species P′ and P″. Advantageously, thephotoswitchable species share identical resonance conditions in terms ofilluminating intensity I₁ ⁰ and I₂ ⁰, these conditions corresponding toequation (90). Advantageously, each of the photoswitchable species isassociated with angular frequencies ω₁ and ω₂ such as defined inequation (91), and corresponding to the resonant angular frequencies ofeach of these species P′ and P″. In particular, the fluorescenceexpressions derived in equations (136) and (137) are similar to equation(107), but with an amplitude that is two times higher in the particularcase of this embodiment of the invention, in which α₁=α₂, allowingselective and simultaneous detection of two separate species P′ and P″.

Advantageously, the periodic modulations applied to the intensities ofthe first illuminating light beam FEX1 and of the second illuminatinglight beam FEX2 are not small with respect to the average intensity ofthese illuminating light beams. They may for example be of the sameorder of magnitude. In the case of large-amplitude periodic modulationsof the intensities of the illuminating light beams FEX1, FEX2, i.e. inthe case where α<1, the inventors have discovered that the conditionsdescribed above remain valid. These validations were carried out bynumerically calculating the various orders of truncated Fourier seriesthe corresponding functions of which were linearized in the precedingcases considering small-amplitude intensity modulation.

The arrows of FIG. 4 illustrate various images Im obtained afterpost-processing of the intensity signal I_(F) ^(out). These images Immay be obtained by demodulating the acquired signal associated with theangular frequency ω_(i) corresponding to the reversibly photoswitchablespecies of interest.

FIG. 5 illustrates a numerical simulation corresponding to thequantification of a species P in the presence of interfering compoundsX. In the absence of information on the various fluorescent speciespresent in a sample, it is possible to optimize the first-orderphase-quadrature fluorescence response I_(F) ^(out). by choosing atriplet (I₁ ⁰, I₂ ⁰, ω) that meets the resonance conditions given inequations (90) and (91), so as to selectively and qualitatively imageone species P among the interfering species X, the latter being definedby the set of parameters (σ_(12,1,X), σ_(21,1,X), σ_(12,2,X),σ_(21,2,X), k_(21,X) ^(Δ)) and of total concentration X_(tot). A speciesX may, in this case, not be photoswitchable, this case corresponding tothe parameters σ_(12,i,X)=σ_(21,i,X)=0 (for i=1 or 2) and k_(21,X)^(Δ)=0. FIG. 5 illustrates the case of a mixture of reversiblyswitchable fluorophore species P only the state 1 of which emits byfluorescence, said species being characterized by the same brightnessQ_(1,j). In this case, a protocol consisting in illuminating, atconstant intensities I_(i) ⁰, gives a signal I_(F) ⁰ proportional to thesum of the contributions of the various fluorophores, such that:

$\begin{matrix}{{{I_{F}^{0} \propto {1_{P}^{0} + {\sum\limits_{X}1_{X}^{0}}}} = {\left( {1_{P}^{0}/P_{tot}} \right)P_{titration}^{0}}}{{where}\text{:}}} & (223) \\{P_{titration}^{0} = {{P_{tot} + {\sum\limits_{X}{\frac{\left( {1_{X}^{0}/X_{tot}} \right)}{\left( {1_{P}^{0}/P_{tot}} \right)}X_{tot}}}} > {P_{tot}.}}} & (224)\end{matrix}$

When the signal I_(F) ⁰ is used to titrate the species P, the result ofthe titration overestimates the total concentration because of thecontributions of the interfering species. In contrast, the first-orderphase-quadrature response to the illumination

may be expressed:

$\begin{matrix}{{{\propto {1_{P}^{1,{{co}\; s}} + {\sum\limits_{X}1_{X}^{1,{{co}\; s}}}}} = {\left( {1_{P}^{1,{{co}\; s}}/P_{tot}} \right)P_{titration}^{1,{{co}\; s}}}}{where}} & (225) \\{P_{titration}^{1,{{co}\; s}} = {P_{tot} + {\sum\limits_{X}{\frac{\left( {1_{X}^{1,{{co}\; s}}/X_{tot}} \right)}{\left( {1_{P}^{1,{{co}\; s}}/P_{tot}} \right)}X_{tot}}}}} & (226)\end{matrix}$

and allows P_(tot) to be determined when the triplet of parameters (I₁⁰,I₂ ⁰,ω) is adjusted under the conditions of resonance for a species P.Specifically, the term 1_(P) ^(1,cos) is maximum whereas the terms 1_(X)^(1,cos) are negligible. The signal generated by the species P ispredominant with respect to that of the other interfering species, andthe titration result P_(titration) ^(1,cos) is approximately equal toP_(tot).

Panel A of FIG. 5 illustrates a numerical simulation of the normalizedamplitudes 1_(X) ⁰/1_(P) ⁰ (illustrated by the gray disks) and of thenormalized amplitudes of 1_(X) ^(1,cos)/1_(P) ^(1,cos) (illustrated bythe black squares) for four equimolar mixtures including the targetspecies characterized by the quintuplet(σ_(12,1),σ_(21,1),σ_(12,2),σ_(21,2),k₂₁ ^(Δ)) and sixteen otherinterfering species. In each sample marked n, these interfering speciescorrespond to sixteen quintuplets the four photochemical parameters ofwhich differ by n orders of magnitude from(σ_(12,1),σ_(21,1),σ_(12,2),σ_(21,2)).

FIG. 6 illustrates the photochemical properties of a set of reversiblyphotoswitchable fluorescent species. For each of the species inquestion, the conditions of resonance according to equations (90) and(91) have been measured and are illustrated by iso-curves of theabsolute value of the normalized amplitude of the first-orderphase-quadrature fluorescence response. Curve (a) corresponds to thespecies “Dronpa”, curve (b) corresponds to the species “Dronpa-2”, curve(c) corresponds to the species “Dronpa-3”, curve (d) corresponds to thespecies “RS-FastLime”, curve (e) corresponds to the species “Padron”,curve (f) corresponds to the species “Kohinoor”, curve (g) correspondsto the species “rsEFGP” and curve (h) corresponds to the species“rsEFGP2”.

In one of the embodiments of the invention, the sample E is illuminatedwith two illuminating light beams of different wavelengths, and each ofthe illuminating light beams is periodically modulated in order to imagea plurality of reversibly photoswitchable species selectively, asillustrated in FIG. 4, the triplet I₁ ⁰, I₂ ⁰, ω_(i) being chosen foreach of the species so as to maximize the component I_(F) ^(out) of thefluorescence radiation.

In one particular embodiment, the conditions of resonance set by the twoaverage intensities of the illuminating light beams, i.e. by therelationship (σ_(12,1)+σ_(21,1))I₁ ⁰=(σ_(12,2)+σ_(21,2))I₂ ⁰, areemployed. Graphically, this solution consists in imaging two reversiblyphotoswitchable species the conditions of resonance of which may beillustrated by points that are substantially dose to the same verticalline in FIG. 6.

One variant of the invention consists in employing these conditions andchoosing two frequencies ω₁ and ω₂ (in the case of detection of twospecies P′ and P″) meeting the conditions of resonance of each of thespecies. In other words, each angular frequency a meets the conditionω=2 (σ_(12,1)+σ_(21,1))I₁ ⁰. This embodiment allows the amplitude ofeach first-order phase-quadrature fluorescence response I_(F) ^(out) tobe maximized.

Another variant of the invention consists in employing conditionsrespecting the relationship (σ_(12,1)+σ_(21,1))I₁⁰=(σ_(12,2)+σ_(21,2))I₂ ⁰, and in choosing two angular frequencies tomodulate the illuminating light beams, each of these angular frequenciesbeing associated with one reversibly photoswitchable species and theratio of said angular frequencies being, for example, strictly higherthan 10 and preferably higher than 100. Specifically, when therelationship (90) is respected, the ratio of the resonant angularfrequencies specific to two species P′ and P″ may be low, for examplelower than 10. In this case, if conditions meeting relationship (91) areemployed, the amplitude I_(F) ^(out) corresponding to each species ismaximized, but the contribution of interference to an amplitudeassociated with a given species prevents an optimal contrast from beingobtained between the species. It is possible, in this variant, to userelationship (106) to choose the angular frequencies used to modulatethe illuminating light beams FEX1, FEX2 so as to obtain a ratio betweenthe angular frequencies that is higher than a predefined value, forexample 10, in order to increase the contrast.

More generally, it is possible to depart from the maximum amplitude ofthe fluorescence signal in order to increase the contrast with respectto one or more interfering species. It is for example possible tomaximize the amplitude of the fluorescence under the constraint ofobtaining a minimum contrast, to maximize the contrast provided aminimum amplitude (generally expressed in percent of the maximumamplitude) is obtained, or even to determine a region of the parameterspace ((ω/I₁, I₁/I₂) ensuring both a sufficiently high amplitude and asufficiently high contrast are obtained. Likewise, in the case where itis sought to detect a single fluorescent species, it may be advantageousto depart from the conditions of resonance in order to improve thecontrast with the interfering fluorescenct species, at the price of adecrease in the amplitude of the signal. Most often however,illumination conditions that ensure that the amplitude of the signal isequal to at least 75%, preferably 80% and even more preferably 90% ofthe maximum achievable signal will be chosen.

FIG. 7 is a set of photographs illustrating an experimental comparisonbetween embodiments of the prior art and an embodiment of the invention.

Panel A of FIG. 7 is a photograph illustrating cell nuclei marked with aspecies P. The photograph was taken, using a prior-art method, byimaging the signal I_(F) ^(out) generated with a first illuminatinglight beam of wavelength λ₁=480 nm, which was periodically modulated,and with a second illuminating light beam of wavelength λ₂=405 nm, theintensity of which remained constant.

Panel B of FIG. 7 is a photograph illustrating the same cell nucleimarked with the same species P. The photograph was taken using aprior-art method, by imaging the signal I_(F) ^(out) generated with afirst illuminating light beam of wavelength λ₁=480 nm, the intensity ofwhich remained constant, and with a second illuminating light beam ofwavelength λ₂=405 nm, which was periodically modulated.

Panel C of FIG. 7 is a photograph illustrating the same cell nucleimarked with the same species P. The photograph was taken using a methodaccording to the invention, by imaging the signal I_(F) ^(out) generatedwith a first illuminating light beam of wavelength λ₁=480 nm, which wasperiodically modulated, and with a second illuminating light beam ofwavelength λ₂=405 nm, which was modulated with the same period and inantiphase.

In panel A of FIG. 7, the intensities have been multiplied by two. Inpanel B of FIG. 7, the intensities have been multiplied by −2. The peakintensities are substantially equal in all the panels of the figure,illustrating the increase in the signal achieved, as illustrated in FIG.3, when an embodiment employing two illuminating light beams that areperiodically modulated in antiphase is used, compared to when only oneperiodically modulated illuminating beam or one periodically modulatedilluminating beam and a second illuminating beam of constant intensityis/are used. The amplitude I_(F) ^(out) measured in prior-artembodiments and/or in embodiments of the invention is algebraic: theabsolute values and/or the signs of the measured I_(F) ^(out) may beused to differentiate between them.

FIG. 8 illustrates detection of the fluorescence image of a cellaccording to one embodiment of the invention. In this example, thenucleus of the cell has been marked with a species P, in the presentcase “Dronpa-2”. The mitochondria of the cell have been marked withanother species P′ “Padron”. The species P′ “Padron” is characterized bya dark state 1 and a fluorescent state 2. In this example, twomodulation angular frequencies were employed. The ratio between the twomodulation angular frequencies was set to 100. A first angularfrequency, n₁₀₀ω(D−2). was associated with the species P′ “Dronpa-2”;this angular frequency was higher than the resonant angular frequency of“Dronpa-2”. A second angular frequency, ω(Padron), was associated withthe species P″ “Padron”; this angular frequency was lower than theresonant angular frequency of “Padron”. The legends “Padron” and “D-2”on the left of the images indicate a demodulation of the fluorescencesignal at the angular frequency associated with “Padron” and with“Dronpa-2”, respectively. The legends “P” and “N” on the right of theimages indicate that the amplitude of I_(F) ^(out) shown is of positivesign (P) or negative sign (N), respectively.

The left-hand column of FIG. 8 illustrates images obtained according toone embodiment of the invention, the cell being illuminated with twoilluminating light beams of different wavelengths, said light beamsbeing modulated in antiphase at the angular frequency n₁₀₀ω(D−2). Thenucleus of the cell is significantly visible in the image correspondingto a positive amplitude of I_(F) ^(out) and to a demodulation at theangular frequency corresponding to D-2.

The middle column of FIG. 8 illustrates images obtained according to oneembodiment of the invention, the cell being illuminated with twoilluminating light beams FEX1, FEX2 of different wavelengths, said lightbeams being modulated in antiphase, at the angular frequency ω(Padron).The mitochondria of the cell are significantly visible in the imagecorresponding to a negative amplitude of I_(F) ^(out) and to ademodulation at the angular frequency corresponding to Padron.

The right-hand column of FIG. 8 illustrates images obtained according toone embodiment of the invention, the cell being illuminated with twoilluminating light beams FEX1, FEX2 of different wavelengths, said lightbeams being modulated with components at the angular frequenciesn₁₀₀ω(D−2) and ω(Padron), each component of the second illuminatinglight beam FEX2 being in antiphase with the corresponding component ofthe first illuminating light beam FEX1. The nucleus of the cell issignificantly visible in the image corresponding to a positive amplitudeof I_(F) ^(out) and to a demodulation at the angular frequencycorresponding to D-2, and the mitochondria of the cell are significantlyvisible in the image corresponding to a negative amplitude of I_(F)^(out) and to a demodulation at the angular frequency corresponding toPadron.

FIG. 9 illustrates a system implementing a method according to oneembodiment of the invention. This system, which is illustrated by way ofnonlimiting example, comprises two light sources SLM1 and SLM2 that eachconsist of a light-emitting diode. The light source SLM1 is suppliedwith power by a power source AM1 and the light source SLM2 is suppliedwith power by a power source AM2. The modulation of each of the lightsources SLM1 and SLM2 is obtained by modulating the respective suppliedelectrical power by means of a function generator GF having twoindependent outputs. Since the emission of the light-emitting diodes iswideband, the beams FEX1 and FEX2, emitted by SLM1 and SLM2,respectively, are collimated by lenses, then filtered by two opticalfilters before being directed onto a sample consisting of a microfluidicdevice DMF; for the sake of simplicity, the optical filters have notbeen shown in the figure. The illuminated sample is observed, via itsback side, with an objective OBJ that collects the fluorescenceradiation and focuses it into a beam FLU. The latter is filtered (filterF2) and directed, via a mirror M and a lens LF, onto the sensor of avideo camera CAM. A computer comprises a processor PR that controls thevideo camera CAM so as to detect in phase quadrature, such as describedabove. Advantageously, the acquisition frequency of the video camera iscommensurable with the modulation frequency of the sources FEX1, FEX2.To achieve a simple detection and/or simple titration, without imaging,the video camera CAM may be replaced by a point light sensor.

1. A method for detecting at least one reversibly photoswitchablefluorescent species, including the following steps: (a) illuminating asample containing said at least one said reversibly photoswitchablefluorescent species with a first illuminating light beam, of wavelengthλ₁, and periodically modulated at an angular frequency ω, and with asecond illuminating light beam, of λ₂ different from λ₁, periodicallymodulated at said angular frequency ω; (b) detecting fluorescenceradiation emitted by said sample thus illuminated; and (c) extractingthe amplitude (I_(F) ^(out)) from the component of the intensity of saidfluorescence radiation that has the same periodicity as saidperiodically modulated first illuminating light beam and that is inphase quadrature therewith; said second illuminating light beam beingmodulated in antiphase with respect to said first illuminating lightbeam; and the average intensity of said first illuminating light beam,the average intensity of said second illuminating light beam, and theirangular frequency ω being chosen so as to get close to a maximum of saidamplitude of the intensity component of said fluorescence radiation. 2.The method as claimed in claim 1, wherein at least one said reversiblyphotoswitchable fluorescent species has a first and second chemicalstate, at least one of said states being fluorescent, said or each saidreversibly photoswitchable fluorescent species being capable of beingconverted from said first state to said second state via a firstphoto-induced reaction, then of returning to said first state via asecond photo-induced reaction, and wherein said first illuminating lightbeam has an average intensity I₁ ⁰ and is modulated at an angularfrequency ω and said second illuminating light beam has an averageintensity I₂ ⁰ with:(σ_(12,1)+σ_(21,1))I ₁ ⁰=(σ_(12,2)+σ_(21,2))I ₂ ⁰andω=2(σ_(12,1)+σ_(21,1))I ₁ ⁰ where σ_(12,1)I₁ ⁰ and σ_(21,1)I₁ ⁰ are therate constants of said first and said second reactions photo-induced bysaid first illuminating light beam, respectively; and where σ_(12,2)I₂ ⁰and σ_(21,2)I₂ ⁰ are the rate constants of said first and said secondreactions photo-induced by said second illuminating light beam,respectively.
 3. The method as claimed in claim 1, wherein the averageintensity of said first illuminating light beam, the average intensityof said second illuminating light beam, and their angular frequency ωare also chosen so as to ensure a minimum contrast between saidamplitude of the intensity component of said fluorescence radiation andthe amplitude of a fluorescence intensity component having the sameperiodicity generated by an interfering species.
 4. A method fordetecting at least two reversibly photoswitchable fluorescent specieshaving different dynamic properties, including the following steps: (a)illuminating a sample containing each said reversibly photoswitchablefluorescent species with a first illuminating light beam of wavelengthλ₁ and periodically modulated with a first function summing at least twofirst illuminating components that are modulated with angularfrequencies ωi, each said angular frequency ωi of each said firstilluminating component being associated with one said reversiblyphotoswitchable fluorescent species, and being different from the one ormore other said angular frequencies ωi; and illuminating the sample witha second illuminating light beam, of wavelength λ₂ different from λ₁,and periodically modulated with a second function summing at least twosecond illuminating components that are modulated with said angularfrequencies ωi, each said angular frequency ωi of each said secondilluminating component being equal to a said angular frequency ωi of asaid first illuminating component; (b) detecting fluorescence radiationemitted by said sample thus illuminated; (c) extracting each amplitude(I_(F) ^(out)) of the component of the intensity of said fluorescenceradiation that has the same angular frequency ωi as each saidilluminating component, and that is in phase quadrature with each saidfirst illuminating component; for each said angular frequency ω_(i),each said second illuminating component modulated with said angularfrequency ω_(i) being in antiphase with respect to each said firstilluminating component modulated with said angular frequency ω_(i); andthe average intensity of said first illuminating light beam, the averageintensity of said second illuminating light beam, and said angularfrequencies being chosen so as to get close to a maximum of each saidamplitude of the intensity component of said fluorescence radiation. 5.The method as claimed in claim 4, wherein each said reversiblyphotoswitchable fluorescent species has a first and a second chemicalstates, at least one of said states being fluorescent, each saidreversibly photoswitchable fluorescent species being capable of beingconverted from said first state to said second state via a firstphoto-induced reaction, then of returning to said first state via asecond photo-induced reaction, and wherein said first illuminating lightbeam has an average intensity I₁ ⁰ and is periodically modulated with asaid first function, and said second illuminating light beam has anaverage intensity I₂ ⁰ with for each said reversibly photoswitchablefluorescent species:(σ_(12,1)+σ_(21,1))I ₁ ⁰=(σ_(12,2)+σ_(21,2))I ₂ ⁰ where σ_(12,1)I₁ ⁰ andσ_(21,1)I₁ ⁰ are the rate constants of said first and said secondreactions photo-induced by said first light beam illuminating saidspecies, respectively; and where σ_(12,2)I₂ ⁰ and σ_(21,2)I₂ ⁰ are therate constants of said first and said second reactions photo-induced bysaid second light beam illuminating said species, respectively.
 6. Themethod as claimed in claim 5, wherein, for each said angular frequencyω_(i) corresponding to one said reversibly photoswitchable fluorescentspecies:ω_(i)=2(σ_(12,1)+σ_(21,1))I ₁ ⁰ where σ_(12,1)I₁ ⁰ and σ_(21,1)I₁ ⁰ arethe rate constants of said first and said second reactions photo-inducedby said first light beam illuminating said species, respectively.
 7. Themethod as claimed in claim 5, wherein the ratio between at least twosaid angular frequencies ω_(i) is strictly higher than
 10. 8. The methodas claimed in claim 1, wherein, in said step a), said sample isilluminated by at least one substantially monochromatic illuminatinglight beam.
 9. The method as claimed in claim 1, wherein said steps b)and c) are implemented via synchronous detection of said fluorescenceradiation.
 10. The method as claimed in claim 1, also including thefollowing step: d) determining the concentration of said or at least onesaid reversibly photoswitchable fluorescent species from the componentof the intensity of said fluorescence radiation which is extracted insaid step c).
 11. The method as claimed in claim 1, wherein said or atleast one said reversibly photoswitchable fluorescent species is chosenfrom: a photochromic fluorescent protein; and a complex of a biomoleculewith a fluorogenic probe.
 12. The method as claimed in claim 1, whereinthe sample contains biological material.
 13. The method as claimed inclaim 1, wherein a said illuminating light beam comprises an amount ofdaylight and wherein said amount of daylight is included in the lightintensity received by said reversibly photoswitchable fluorescentspecies but remains less than or equal to the average intensities ofsaid illuminating light beams. A fluorescence-imaging methodimplementing a detecting method as claimed in claim
 1. 15. The method asclaimed in claim 14, wherein said sample may comprise a living organism,and wherein at least one element chosen from the presence andconcentration of a said reversibly photoswitchable fluorescent speciesis measured on the basis of the component of the intensity of saidfluorescence radiation which is extracted in said step c), withouttaking a sample of said living organism.